Parabola in Gardening Scenario

Grace is designing a garden that features a beautiful parabolic archway that opens upwards. What is the standard form of the equation that represents this parabolic archway?

• y = a(x - h)² + k, where a > 0

• y = ax² + bx + c, where a > 0

• y = a(x - h)² + k, where a = 0

• y = a(x + h)² + k, where a < 0

Sophia is designing a parabolic garden path that can be modeled by the equation y = 2x^2 + 4x + 1. She wants to convert this equation to vertex form to better understand the shape of her path.

• y = 2(x - 1)^2 + 3

• y = 2(x + 2)^2 + 5

• y = 2(x - 1)^2 - 2

• y = 2(x + 1)^2 - 1

Charlotte is designing a garden in the shape of a parabola, represented by the equation y = -3(x - 2)^2 + 5. Identify the highest point, or vertex, of her garden.

• (5, 2)

• (2, 5)

• (2, 0)

• (0, 5)

Priya is designing a garden in the shape of a parabola defined by the equation y = (1/4)(x - 2)^2 + 3. What is the focus of her garden's parabolic shape?

• (2, 3)

• (2, 4)

• (1, 4)

• (3, 4)

Aiden is designing a water fountain in the shape of a parabola described by the equation y = (1/4)(x + 1)^2 - 2. To ensure the fountain functions properly, he needs to determine the directrix of the parabola. What is the equation of the directrix?

• y = -4

• y = -1

• y = -3

• y = -2

Aiden is designing a parabolic slide for a playground, and the shape of the slide can be described by the equation y = 5x^2 - 10x + 3. What is the axis of symmetry for his slide design?

• x = 1

• x = -1

• x = 0

• x = 2

Nora is designing a parabolic garden path that can be represented by the equation y = x^2 - 6x + 8. She wants to convert this equation into vertex form to better understand the shape of her garden path.

• y = (x + 3)^2 + 1

• y = (x - 3)^2 - 1

• y = (x - 2)^2 + 4

• y = (x - 4)^2 - 2

Luna is creating a decorative garden arch in the shape of a parabola described by the equation y = -2x^2 + 4x + 1. Identify the direction in which the arch opens.

• downwards

• to the right

• upwards

• to the left

Zoe is designing a parabolic garden fountain that opens up at the point (4, 2). The shape of the fountain follows the equation y = (1/8)(x - 4)^2 + 2. What is the distance between the focus and the directrix of the fountain's parabolic shape?

• 4

• 1

• 3

• 2

Find the coordinates of the vertex for the parabola given by y = 3(x + 1)^2 - 7.

• (0, -7)

• (1, -7)

• (-1, 0)

• (-1, -7)